cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A189055 Primes of the form (k+1)^11 - k^11.

Original entry on oeis.org

313968931, 6612607849, 68618940391, 2257404775627, 26360313735014491, 130898631716248441, 11736367906285382977, 28945284114821573731, 229761141540921525811, 202978059247932180748537, 228398127589553102936371, 476213535986962784582617, 1627839264198988265272849, 3421374091098795513254497
Offset: 1

Views

Author

David Cushing, Dec 19 2012

Keywords

Comments

All prime numbers which are the difference of integers raised to the 11th power have this form. Values of n in A211184.

Links

Programs

  • Python
    from itertools import count
primes = Primes()
def diff_pow(i, n):
  return (i+1)**n - i**n
def diff_pow_primes(n, limit=range(1000)):
  pows = [diff_pow(i, n) for i in limit]
  return [p for p in pows if p in primes]
diff_pow_primes(11, count())

A221983 Number of primes of the form (x+1)^11 - x^11 less than 10^n.

Original entry on oeis.org

1, 2, 3, 3, 4, 4, 4, 4, 5, 6, 6, 8, 9, 9, 9, 12, 15, 18, 24, 30, 35, 41, 46, 66, 83, 104, 133, 166, 195, 247, 314, 400, 475, 589, 709, 855, 1046, 1313, 1604, 1998, 2468, 3029, 3681, 4518, 5581, 6920, 8629, 10647, 13122, 16214, 19894, 24644, 30569, 37864, 46927
Offset: 9

Views

Author

Vladimir Pletser, Feb 02 2013

Keywords

Comments

Number of primes less than 10^n and equal to the difference of two consecutive eleventh powers (x+1)^11 - x^11 = 11x(x+1)(x^2+x+1)( x(x+1)(x^2+x+1)(x^2+x+3)+1) + 1 (A189055). Values of x = A211184. Sequence of number of primes less than 10^n and of the form (x+1)^11 - x^11 have similar characteristics to similar sequences for natural primes (A006880), cuban primes (A113478) and primes of the form (x+1)^p - x^p for p = 5 (A221846) and p = 7 (A221977).

Links

Programs

  • Mathematica
    nn = 40; t = Table[0, {nn}]; n = 0; While[n++; p = (n + 1)^11 - n^11; p < 10^nn, If[PrimeQ[p], m = Ceiling[Log[10, p]]; t[[m]]++]]; Accumulate[t] (* T. D. Noe, Feb 04 2013 *)

A221984 Number of primes of the form (x+1)^11 - x^11 having n digits.

Original entry on oeis.org

1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 3, 3, 3, 6, 6, 5, 6, 5, 20, 17, 21, 29, 33, 29, 52, 67, 86, 75, 114, 120, 146, 191, 267, 291, 394, 470, 561, 652, 837, 1063, 1339, 1709, 2018, 2475, 3092, 3680, 4750, 5925, 7295, 9063, 11174, 14034, 17294, 21208
Offset: 9

Views

Author

Vladimir Pletser, Feb 02 2013

Keywords

Comments

Number of primes having n digits and equal to the difference of two consecutive eleventh powers (x+1)^11 - x^11 = 11x(x+1)(x^2+x+1)[ x(x+1)(x^2+x+1)(x^2+x+3)+1] +1 (A189055). Values of x = A211184. Sequence of number of primes having n digits and of the form (x+1)^11 - x^11 have similar characteristics to similar sequences for natural primes (A006879), cuban primes (A221792) and primes of the form (x+1)^p - x^p for p = 5 (A221847) and p = 7 (A221978).

Links

Programs

  • Mathematica
    nn = 40; t = Table[0, {nn}]; n = 0; While[n++; p = (n + 1)^11 - n^11; p < 10^nn, If[PrimeQ[p], m = Ceiling[Log[10, p]]; t[[m]]++]]; t (* T. D. Noe, Feb 04 2013 *)

A221985 Partial sums of primes of the form (n+1)^11 - n^11.

Original entry on oeis.org

313968931, 6926576780, 75545517171, 2332950292798, 26362646685307289, 157261278401555730, 11893629184686938707, 40838913299508512438, 270600054840430038249, 203248659302772610786786, 431646786892325713723157, 907860322879288498305774, 2535699587078276763578623
Offset: 1

Views

Author

Vladimir Pletser, Feb 02 2013

Keywords

Comments

Partial sums of primes equal to the difference of two consecutive eleventh powers (x+1)^11 - x^11 = 11x(x+1)(x^2+x+1)[ x(x+1)(x^2+x+1)(x^2+x+3)+1] +1 (A189055). Values of x = A211184. Number of primes equal (x+1)^11 - x^11 < 10^(n) in A221983. Partial sums of number of primes of the form (x+1)^11 - x^11 have similar characteristics to similar sequences for natural primes (A007504), cuban primes (A221793) and primes of the form (x+1)^p - x^p for p = 5 (A221848) and p = 7 (A221979).

Links

Programs

  • Mathematica
    Accumulate[Select[Differences[Range[300]^11],PrimeQ]] (* Harvey P. Dale, Mar 24 2023 *)

A221986 Number of primes of the form (x+1)^11 - x^11 with x <= 10^n.

Original entry on oeis.org

0, 3, 9, 46, 479, 3711, 30830
Offset: 0

Views

Author

Vladimir Pletser, Feb 02 2013

Keywords

Comments

Number of primes equal to the difference of two consecutive eleventh powers (x+1)^11 - x^11 = 11x(x+1)(x^2+x+1)(x(x+1)(x^2+x+1)(x^2+x+3)+1) +1 (A189055). Values of x = A211184. Sequence of number of primes of the form (x+1)^7 - x^7 with x <= 10^n have similar characteristics to similar sequences for natural primes, cuban primes (A221794) and primes of the form (x+1)^p - x^p for p = 5 (A221849) and p = 7 (A221980).
Showing 1-5 of 5 results.

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